A) \[{{x}^{2}}+{{y}^{2}}+ax=0\]
B) \[{{x}^{2}}+{{y}^{2}}-ax=0\]
C) \[{{x}^{2}}+{{y}^{2}}+ay=0\]
D) \[{{x}^{2}}+{{y}^{2}}-ay=0\]
Correct Answer: B
Solution :
Let \[(h,k)\] be the co-ordinates of the centre of circle of which the given chord is the diameter. Then \[(h,k)\] be mid point of the chord, so, its equation is \[S=T.\] \[{{h}^{2}}+{{k}^{2}}-2ah=hx+ky-a(x+h)\] \[\Rightarrow \]\[x(h-a)+ky={{h}^{2}}+{{k}^{2}}-ah\] If it passes through \[(0,0),\] therefore \[{{h}^{2}}+{{k}^{2}}-ah=0\]and the locus of \[(h,k)\] is\[{{x}^{2}}+{{y}^{2}}-ax=0.\]
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